The gun should be checked by someone who is trained and understands S&W pistols.
I'll offer some comments about what you've posted in the thread, for the purpose of conversation, but the gun should still be checked by someone trained to repair S&W pistols.
Was the hammer "decocking" during firing? In other words, were the safety/decocking levers in the DOWN/ON SAFE position after each shot? Did you have to lift the safety lever after each shot was fired in order to fire the next round?
If so, it's possible that the wrong spring was installed in the decocker body assembly when you reassembled the gun. This is a mistake that armorers are warned about because it can be easy to switch the ambi lever spring for the decocker body spring.
If switched, the lighter tension ambi lever spring doesn't have the strength to keep the assembly from rotating during live-fire when the slide is cycling. Armorers are repeatedly warned not to mistakenly switch the springs, but it sometimes happens. I've watched new armorers do it during classes. I've even seen an armorer do it at the bench when working on a duty gun.
For that matter, one time I even found a gun which had the wrong plunger in the decocker body, an ambi lever plunger, which caused the decocking effort to be nasty, hard and gritty. Fortunately, the wrong plunger had not yet damaged the inside surface of the slide where the decocking body plunger was intended to ride smoothly along the surface and I installed the correct plunger.
I knew of an agency where a new armorer mistakenly switched the decocking body & ambi lever plunger springs one time. Fortunately, the resulting single-shot-remains-on-safe condition was discovered on the range ... although the guns had been carried on-duty for a while before it was discovered.
The light ambi lever spring is painted a light blue (when still new and clean) and can easily be compressed between fingertips ... as long as you don't let it slip and fly away to disappear in the carpet or behind the dark recesses of the workbench.
The heavier decocker body spring is unpainted and cannot be easily compressed between the fingers. (This is how the armorer who asked for my help discovered the mistake. He was having a hard time trying to compress the decocker body spring deeply enough in the slide's ambi lever spring hole to slip the lever back on over it. He asked for my help and I saw he had the wrong spring.)
FYI ... There was a change made to the ambi lever plunger (described in narrative of manual excerpt), which also required a change in the ambi levers (to accept the larger plunger head).
Here's a couple of thumbnails of info from an armorer manual describing the different parts being discussed.
If the wrong plunger spring is not in the decocker body ...
The usual probable causes of the hammer following the slide forward can be a damaged sear, sear spring or single action cocking notch(es) on the hammer. These things may result in double taps or bursts.
I'd also check to see if the sear had been installed so that the bottom was on the wrong side of the sear spring. It should be in front of the sear spring, not behind it (front & rear/behind relative to the front and rear of the gun's normal orientation). The armorer manual states it in another way, that the sear should be behind the sear spring when viewing from the rear of the frame. (Describing it from the viewer perspective, when the viewer is located to the rear of the frame, has always seemed a bit less precise to me than describing it from the perspective of the normal orientation of the gun itself, front and back, but that's just me and I don't write the manual.
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However you describe it, the top of the sear spring pushes forward against the bottom of the sear, which tensions the pivoting sear rearward at the top, which is what keeps the the sear nose under the hammer's single action cocking notches to hold the hammer in single action.
You greased the internals?
FWIW, the 'internals' of a S&W traditional double action pistol are not recommended lubrication points.
Armorers are told that as the gun is reassembled the parts may be wiped with a lightly oiled patch. A drop of oil (or grease, if preferred) should be applied to the barrel hood (front), the barrel muzzle (around the outside circumference of the barrel), both sides of the hammer and both left & right side rails. The recoil guide rod and recoil spring can also be wiped with a lightly oiled patch. (Different environmental conditions and operational needs may require some modified maintenance procedures and S&W may make recommendations as appropriate.)
There are things that can be done wrong when reassembling a S&W pistol.
Just my thoughts.
If this was reported to be happening with one of the guns belonging to my agency I'd certainly want to examine it to figure out what was occurring, and preferably talk to the person who experienced the problem when it happened. Weird things can happen.
